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Transcript of Chapter 5. Fluidization Chapter 5. Fluidization 5.1 Fundamental * ®â€‌p vs. U...

• Chapter 5. Fluidization

5.1 Fundamental

* Δ p vs. U Figure 5.1

Minimum (incipient) fluidization, U mf

From force balance

Net downward force

Δp= ( 1- ε )( ρ p- ρ g )H (1)

Net upward force

Δp H

= 150 ( 1- ε ) 2

ε 3 μU

x 2sv + 1.75

1- ε

ε 3 ρ gU

2

x sv (2)

Equating (1) and (2) at U=U mf

Ar=150 ( 1- ε ) ε 3

Re mf+1.75 1 ε 3 Re

2 mf

where Ar≡ ρ gx

3 sv (ρ p- ρ f)g

μ 2 , Archimedes number

Re mf= ρ fU mfx sv μ

ε= 0.4, usually

More practically,

Wen and Yu(1966) for x sv > 1 0 0 μm

Ar= 1056Remf+159Re 2 mf

Baeyens and Geldart(1974) for x < 1 0 0 μ m

U mf= ( ρ p- ρ f)

0.934g 0.934x 1.8

1110μ 0.87ρ 0.066f

5.2 Relevant Powder and Particle Properties

• - Absolute density: materials property

- Particle density: Figure 5.2

- Bed density

* Sieve diameter, x p , x v= 1.13x p

mean x p= 1

∑m i/x i

5.3 Bubbling and Non-Bubbling Fluidization

Types of Fluidization

Various types of fluidized beds

- Bubbling fluidized bed : Figure 5.3 for Group B particles

• - Liquid fluidization: Figure 5.4

5.4 Classification of Powders

Geldart(1974) Figure 5.6

Table 5.1

Group A : Nonbubbling for U m f < U < U m b

where

U mb= 2.07 exp (0.716F ) [ xρ 0.06g μ 0.347 ]

where F : fraction of powder less than 45 μm

Bubbling for U > U m b

Maximum bubble size

d Bv, max = 2 g

(U T2.7 ) 2

Group B : Bubbling for U > U m f

No maximum in bubble size

Slugging ( d B≥ 1 3 D) - Figure 5.8 (right)

Tagi and Muchi (1952)

In order to avoid slug formation

( H m f D )≤

1.9

( ρ p x p ) 0.3

Slug forms when ( H m f D ) >

1 . 9

( ρ p x p ) 0 . 3

and

U > U mf+0.16(1.3 4D 0.175-H mf)

2+ 0.07( gD ) 1/2

Group D : Spoutable

• Group C : Subject to channeling in large diameter-bed

5.5 Expansion of a Fluidized Bed

(1) Nonbubbling Fluidized Bed

Upward superficial fluid velocity(or volumetric flux)

U= U Tε 2f(ε) =U T ε

n

For Re p≤0.3, n= 4.65

For Re p≥500, n= 2.4

Assuming conservation of bed mass, M B

M B= (1- ε )ρ pAH

∴ ( 1- ε 1 )ρ pAH 1 = ( 1- ε 2 )ρ pAH 2

∴ H 2 H 1

= 1- ε 1 1- ε 2

Worked Example 5.1

(2) Bubbling Fluidized Bed

The bed is assumed to consist of two phases:

- Dense (particulate, emulsion) phase : a state of minimum

fluidization

- Lean (bubble) phase : flow of gas in excess of minimum

fluidization as bubbles

Gas flow as bubbles= Q-Qmf= (U-Umf )A

Gas flow in the emulsion phase=Qmf=UmfA

ε B=

H-Hmf H

= QB AU B

= U-Umf U B

* Mean bed voidage, 1- ε= ( 1- ε B )( 1- ε mf)

* Bubble Size and Rise Velocity

U B= Φ B (gd Bv ) 1/2

where Φ B= function of D

• For group B

d Bv= 0.54

g 0.2 (U-U mf )

0.4(L+4N - 1/2 ) 0.8

where N : the number of holes/m 2

L : distance above the distributor

5.6 Entrainment

- Carryover, elutriation

Zone above fluidized bed (Freeboard) - Figure 5.11

- Splash zone

- Transport disengagement zone

Transport disengagement height,

TDH from Figure 5.12 or

TDH= 4.47d 0.5Bvs

- Dilute-phase transport zone

Worked Example 5.1

Instantaneous entrainment rate of size x i

R i=- d dt

(MBmBi)=K * ihAm Bi

where M B: total mass of solids in the bed

A: area of bed surface

m Bi: fraction of bed mass with size x i at time t

K *ih: elutriation constant

Total rate of entrainment

R T=- d dt

[∑(MBm Bi)]=∑K * ihAm Bi

K * i∞ : K *ih above TDH - (5.45) and (5.46)

Worked Example 5.2

• 5.7 Heat transfer in Fluidized Bed

Heat transfer between particles and gas

Nu= 0.03Re 1.3p ( Re p≺50)

where Nu= h gpx

k g

L 0.5 : L for T g-T s T g0-T s

=0.5

Very short(0.95mm～5mm)

Heat transfer between surface and bed

h = h p c + h g c + h r

Figure 5.14: h pc is controlled by k g

Figure 5.15: maximum occurs by blanket of bubbles

When U > ( 2 ∼ 3 )×U m f

For group B powders

h max = 35.8k 0.6 g

ρ 0.2 p

x 0.36

, W/m2K

For group A powders

Nu max = 0.157Ar 0.475

5.8 Applications of Fluidized Beds

- Liquid-like behavior, easy to control and automate

- Rapid mixing, uniform temperature and concentration

- Resists rapid temperature changes, hence responds slowly to

changes in operating conditions and avoids temperature runaway

• with exothermic reactions

- Circulate solids between fluidized beds for heat exchange

- Applicable for large or small scale operations

- Heat and mass transfer rates are high, requiring smaller

surfaces

- Bubbling beds are difficult to predict and are less efficient

- Rapid mixing of solids causes nonuniform residence times for

continuous flow reactors

- Particle comminution(breakup) is common

- Pipe and vessel walls erode to collisions by particles

(1) Physical Processes

Drying / Mixing / Granulation / Coating / Heat exchanger/

Figure 5.17

(2) Chemical Processes

Table 5.2

Figure 5.18 Fluidized catalytic cracker

5.9 A Simple Model for the Bubbling Fluidized Bed

Reactor

Figure 5.19

Orcutt et al(1962)

Form the overall mass balance on the reactant + shell mass balance

1- C H C 0

= (1- βe - χ )-

( 1- βe - χ ) 2

kH mf( 1- ε p )

U + (1- β e -

χ )

• C BH= C P+ (C 0-C P) exp [- χ ]

C P= C 0[U-(U-U mf )e

- χ]

kH mf(1- ε P )+ [U (U-U mf)e - χ]

CH= UmfC P+(U-Umf)CBH

U

where C 0 : concentration of reactant at distributor

C H : concentration of reactant leaving the reactor(H)

C B : concentration of the reactant in the bubble phase

C P : concentration of the reactant in the particulate phase

β= U-Umf U

and χ= K cH

U B

where K c: mass transfer coefficient of the reactant from particulate

phase

Figure 5.20

Worked Example 5.3